The refugee women also doused the hostage with petrol, according to witnesses and security officials on Wednesday.
The 17 are believed to be demanding better rights for the thousands of refugees who fled the separatist region of Abkhazia.
Fire crews and police have surrounded the building, which houses the city’s new underground metro construction offices.
The official was seized after talks failed between the women and government officials. Tass news agency said several hostages were being held.
Tens of thousands of refugees of Georgian origin fled Abhkazia after separatist rebels declared independence in 1992.
Even more have left the region in the last few years, despite a Russian military buffer zone that separates the ethnic groups.